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Comparison and optimization of smoothing procedures for small‐angle X‐ray scattering curves. Polynomial fitting and modified frequency filtering
Author(s) -
Müller J. J.,
Damaschun G.
Publication year - 1979
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889879012450
Subject(s) - smoothing , polynomial , curve fitting , scattering , filter (signal processing) , mathematics , algorithm , optics , mathematical analysis , computer science , physics , statistics , computer vision
The filter theory allows one to compare the efficiencies of smoothing procedures widely used in the field of small‐angle X‐ray scattering. This method is demonstrated for polynomial fitting and modified frequency filtering. Optimized and objective smoothing parameters are determined for both procedures through the knowledge of variance reduction factors, transfer functions of the filters, the largest value of the spatial frequencies of the scattering curve and the distortions caused by the smoothing procedures. The comparison of the efficiency of polynomial fitting and frequency filtering clearly shows the superiority of the latter; therefore, this method has to be preferred.